1. Field of the Invention
The present invention relates to an FIR filter and method of setting coefficients of the FIR filter that are necessary for digital signal processing.
2. Description of the Related Art
In the digital signal processing for picture and/or voice, filter processing is often used. Linear-phase FIR (Finite Impulse Response) filter is often utilized as the filter for digital signal processing of picture and/or voice in that the linear-phase FIR filter has the characteristics that its number of taps is finite and has a linear-phase.
FIG. 1 is a view illustrating circuit configuration of a transversal type filter of the linear-phase FIR filter.
The linear-phase FIR filter 1, as illustrated in FIG. 1, has (n-1) delay units 2-1 to 2-(n-1) that constitute a shift register connected to an input terminal TIN with cascade connection, n multipliers 3-1 to 3-n for multiplying a signal input to the input terminal TIN and output signals of respective delay units 2-1 to 2-(n-1) by filter coefficients h (0) to h (n-1) respectively, and an adder 4 for adding n output signals of the multipliers 3-1 to 3-n to output to an output terminal TOUT.
As a typical method for designing such the linear-phase FIR filter, for instance, these are known Remez Exchange algorithms which Parks, T. W. and McCleLLan, J. H. et al. apply it to the linear-phase FIR filter (Parks, T. W. and McClellan, J. H.: “Chebyshev Approximation for Non-recursive Digital Filters with Linear Phase”, IEEE Trans. Circuit Theory, CT-19, 2, pp. 189-194, 1972, as well as Rabiner, L. R., McClellan, .J .H. and Parks, T. W.: “FIR Digital Filter Design Techniques Using Weighted Chebyshev Approximation”, Proc. IEEE, Vol 63, April, pp.595-610, 1975).
The Remez Exchange algorithm is an algorithm in which a weighted approximation error is approximated such that the weighted approximation error is made to configure equi-ripple to the desired amplitude characteristics.
There is known a resolution conversion of a picture that utilizes the sampling rate conversion as the application of the filter processing using the linear-phase FIR filter.
In this resolution conversion, multi-rate filter which has an interpolator, a decimeter and the linear-phase FIR filter as element-technique is employed (see, P. P. Vaidyanathan: “Multirate System and Filter Banks”, Prentice Hall, 1992).
In use of the multi-rate filter, generally, the linear-phase FIR filter is made to be used in such a way as to execute a polyphase-sort (dissolution) in order to adjust the interpolator. Both the interpolator and the decimeter form periodic time invariance systems, thus having different characteristics from the time invariance system.
Distortion so called as the chessboard distortion on a lattice occurs in the resolution conversion of the picture caused by the periodic time invariance property of the interpolator.
Accordingly, Harada, and Takaie considered the condition for avoiding such chessboard distortion from the viewpoint of a zero-point arrangement of a filter (see, Yasuhiro Harada, Hitoshi Kiya,: “Multi-rate Filter without Accompanying Chessboard Distortion and its Zero-point Arrangement” The technical Report of IEICE CAS96-78, pp1-6, 1997-01).
A transfer function H (z) for the multi-rate filter without accompanying the chessboard distortion will be discussed. The transfer function H (z) is capable of being found in such a way as to multiply a transfer function K (z) of the linear-phase FIR filter (hereinafter referred to as an equalizer) designed by a method in some kind by the transfer function Z (z) of the zero-point in order to avoid the chessboard distortion later.H(z)=Z(z)·K(z)   (1) Z(z)=1÷z−1+z−2+···+z−(u−1)   (2) 
Here, a linear-phase FIR filter fixed beforehand such as the transfer function Z (z) of the zero-point for avoiding the chessboard distortion is called as a pre-filter.
FIG. 2 shows an example of a frequency response of the multi-rate filter and a weighted approximation error, in which the chessboard distortion is avoided by multiplying the equalizer designed by the use of Remez Exchange algorithms and the pre-filter.
However, it suffers from the disadvantage in the avoiding method of the chessboard distortion according to the aforementioned method.
Namely, as illustrated in FIG. 2C, in the multi-rate filter having the transfer function H (z) designed depending on the conventional method, the equi-ripple of the weighted approximation error designed depending on the Remez Exchange algorithms is not established.
Further, as illustrated in FIG. 2B, the multi-rate filter designed depending on the conventional method, has a gain of its pass band with non-fixed value in which a right end is attenuated.
If the resolution conversion is executed using such filter, contours of picture appears fuzzy and thus, adversely affect quality of the picture.
The attenuation of this pass band cannot be avoided even though the number of coefficient of filter is increased.